Graph the equation y=-1/8x^2+x-4

Suppose the proportion X of surface area in a randomly selected quadrat that is covered by a certain plant has a standard beta d

dem82 [27]

Answer:

(a) The value of E (X) is 4/7.

The value of V (X) is 3/98.

(b) The value of P (X ≤ 0.5) is 0.3438.

Step-by-step explanation:

The random variable X is defined as the proportion of surface area in a randomly selected quadrant that is covered by a certain plant.

The random variable X follows a standard beta distribution with parameters α = 4 and β = 3.

The probability density function of X is as follows:

$f(x) = \frac{x^{\alpha-1}(1-x)^{\beta-1}}{B(\alpha,\beta)} ; \hspace{.3in}0 \le x \le 1;\ \alpha, \beta > 0$

Here, B (α, β) is:

$B(\alpha,\beta)=\frac{(\alpha-1)!\cdot\ (\beta-1)!}{((\alpha+\beta)-1)!}$

$=\frac{(4-1)!\cdot\ (3-1)!}{((4+3)-1)!}\\\\=\frac{6\times 2}{720}\\\\=\frac{1}{60}$

So, the pdf of X is:

$f(x) = \frac{x^{4-1}(1-x)^{3-1}}{1/60}=60\cdot\ [x^{3}(1-x)^{2}];\ 0\leq x\leq 1$

(a)

Compute the value of E (X) as follows:

$E (X)=\frac{\alpha }{\alpha +\beta }$

$=\frac{4}{4+3}\\\\=\frac{4}{7}$

The value of E (X) is 4/7.

Compute the value of V (X) as follows:

$V (X)=\frac{\alpha\ \cdot\ \beta}{(\alpha+\beta)^{2}\ \cdot\ (\alpha+\beta+1)}$

$=\frac{4\cdot\ 3}{(4+3)^{2}\cdot\ (4+3+1)}\\\\=\frac{12}{49\times 8}\\\\=\frac{3}{98}$

The value of V (X) is 3/98.

(b)

Compute the value of P (X ≤ 0.5) as follows:

$P(X\leq 0.50) = \int\limits^{0.50}_{0}{60\cdot\ [x^{3}(1-x)^{2}]} \, dx$

$=60\int\limits^{0.50}_{0}{[x^{3}(1+x^{2}-2x)]} \, dx \\\\=60\int\limits^{0.50}_{0}{[x^{3}+x^{5}-2x^{4}]} \, dx \\\\=60\times [\dfrac{x^4}{4}+\dfrac{x^6}{6}-\dfrac{2x^5}{5}]\limits^{0.50}_{0}\\\\=60\times [\dfrac{x^4\left(10x^2-24x+15\right)}{60}]\limits^{0.50}_{0}\\\\=[x^4\left(10x^2-24x+15\right)]\limits^{0.50}_{0}\\\\=0.34375\\\\\approx 0.3438$

Thus, the value of P (X ≤ 0.5) is 0.3438.

8 0

3 years ago

The graph shows a system consisting of a linear equation and a quadratic equation. What is the solution to the system?

Alecsey [184]

Your answer will be:

B: B) (2,11) and (4,3)

Hope I helped!! :)

8 0

3 years ago

Read 2 more answers

Asap! please help i’ll give brainliest

Aleonysh [2.5K]

Answer: 2nd one

Step-by-step explanation: Look at the options. In all of the options, the number of 0's is 3 so you don't have to look for the zero's. Next look at the one's. The first 2 have 2 ones and the next 2 have 3. The number of ones in the data is 2 so you can eliminate the last 2. Then look at the 2's between the top 2. In the first one, there is 2 and in the second one there is only one. In the data table, there is one 2 so the answer has to be the 2nd one. Hope this helps :)

6 0

3 years ago

Clarissa has a budget of $1,200 a month to spend for rent and food. She has already spent $928 this month. Which inequality repr

shtirl [24]

Answer:

1200-928 = 272 for the rest of the month Clarissa has to spend.

Step-by-step explanation:

So we don't want her to go over her budget so we wouldn't choose a greater than option for her so eliminate the first option and the last option. Now we just have the middle two. We want to keep it under 1200 but theres nothing wrong with spending that exact amount each month so I would pick x less than or equal to 272, since we can still equal the total of less than the total and not go over. Option 2 or B.

6 0

2 years ago

Read 2 more answers

A box contains 6 red pens and 4 blue pens. Cory randomly picks a pen from

Monica [59]

Answer:

Hay probabilidad

Step-by-step explanation:

porque hay mas boligrafos rojos que azules

4 0

2 years ago